A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
Answer: C) 3/4
Explanation:
Let A, B, C be the respective events of solving the problem and A , B, CA , B, C be the respective events of not solving the problem. Then A, B, C are independent event
∴A, B, C∴A, B, C are independent events
Now, P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4
P(A)=12, P(B)=23, P(C)= 34PA=12, PB=23, PC= 34
∴∴ P( none solves the problem) = P(not A) and (not B) and (not C)
= P(A∩B∩C)PA∩B∩C
= P(A)P(B)P(C)PAPBPC [∵ A, B, C are Independent]∵ A, B, C are Independent
= 12×23×3412×23×34
= 1414
Hence, P(the problem will be solved) = 1 - P(none solves the problem)
= 1−141-14= 3/4